Solve (frac{(4x)^{2}(y^{3})^0}{-3x^-1y^2})^3

$$( \frac { ( 4 x ) ^ { 2 } ( y ^ { 3 } ) ^ { 0 } } { - 3 x ^ { - 1 } y ^ { 2 } } ) ^ { 3 }$$

Evaluate

$$-\frac{4096x^{9}}{27y^{6}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 0 to get 0.

$$\left(\frac{\left(4x\right)^{2}y^{0}}{-3x^{-1}y^{2}}\right)^{3}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{\left(4x\right)^{2}}{-3\times \frac{1}{x}y^{2}}\right)^{3}$$

Expand \left(4x\right)^{2}.

$$\left(\frac{4^{2}x^{2}}{-3\times \frac{1}{x}y^{2}}\right)^{3}$$

Calculate 4 to the power of 2 and get 16.

$$\left(\frac{16x^{2}}{-3\times \frac{1}{x}y^{2}}\right)^{3}$$

Express -3\times \frac{1}{x} as a single fraction.

$$\left(\frac{16x^{2}}{\frac{-3}{x}y^{2}}\right)^{3}$$

Express \frac{-3}{x}y^{2} as a single fraction.

$$\left(\frac{16x^{2}}{\frac{-3y^{2}}{x}}\right)^{3}$$

Divide 16x^{2} by \frac{-3y^{2}}{x} by multiplying 16x^{2} by the reciprocal of \frac{-3y^{2}}{x}.

$$\left(\frac{16x^{2}x}{-3y^{2}}\right)^{3}$$

Cancel out -1 in both numerator and denominator.

$$\left(\frac{-16x^{2}x}{3y^{2}}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\left(\frac{-16x^{3}}{3y^{2}}\right)^{3}$$

To raise \frac{-16x^{3}}{3y^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-16x^{3}\right)^{3}}{\left(3y^{2}\right)^{3}}$$

Expand \left(-16x^{3}\right)^{3}.

$$\frac{\left(-16\right)^{3}\left(x^{3}\right)^{3}}{\left(3y^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\left(-16\right)^{3}x^{9}}{\left(3y^{2}\right)^{3}}$$

Calculate -16 to the power of 3 and get -4096.

$$\frac{-4096x^{9}}{\left(3y^{2}\right)^{3}}$$

Expand \left(3y^{2}\right)^{3}.

$$\frac{-4096x^{9}}{3^{3}\left(y^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{-4096x^{9}}{3^{3}y^{6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{-4096x^{9}}{27y^{6}}$$

Expand

$$-\frac{4096x^{9}}{27y^{6}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 0 to get 0.

$$\left(\frac{\left(4x\right)^{2}y^{0}}{-3x^{-1}y^{2}}\right)^{3}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{\left(4x\right)^{2}}{-3\times \frac{1}{x}y^{2}}\right)^{3}$$

Expand \left(4x\right)^{2}.

$$\left(\frac{4^{2}x^{2}}{-3\times \frac{1}{x}y^{2}}\right)^{3}$$

Calculate 4 to the power of 2 and get 16.

$$\left(\frac{16x^{2}}{-3\times \frac{1}{x}y^{2}}\right)^{3}$$

Express -3\times \frac{1}{x} as a single fraction.

$$\left(\frac{16x^{2}}{\frac{-3}{x}y^{2}}\right)^{3}$$

Express \frac{-3}{x}y^{2} as a single fraction.

$$\left(\frac{16x^{2}}{\frac{-3y^{2}}{x}}\right)^{3}$$

Divide 16x^{2} by \frac{-3y^{2}}{x} by multiplying 16x^{2} by the reciprocal of \frac{-3y^{2}}{x}.

$$\left(\frac{16x^{2}x}{-3y^{2}}\right)^{3}$$

Cancel out -1 in both numerator and denominator.

$$\left(\frac{-16x^{2}x}{3y^{2}}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\left(\frac{-16x^{3}}{3y^{2}}\right)^{3}$$

To raise \frac{-16x^{3}}{3y^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-16x^{3}\right)^{3}}{\left(3y^{2}\right)^{3}}$$

Expand \left(-16x^{3}\right)^{3}.

$$\frac{\left(-16\right)^{3}\left(x^{3}\right)^{3}}{\left(3y^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\left(-16\right)^{3}x^{9}}{\left(3y^{2}\right)^{3}}$$

Calculate -16 to the power of 3 and get -4096.

$$\frac{-4096x^{9}}{\left(3y^{2}\right)^{3}}$$

Expand \left(3y^{2}\right)^{3}.

$$\frac{-4096x^{9}}{3^{3}\left(y^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{-4096x^{9}}{3^{3}y^{6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{-4096x^{9}}{27y^{6}}$$